Our general goal is to provide better automation in interactive proof assistants such as Coq. We present an interpreter of proof traces in first-order multi-sorted logic with equal...
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing d...
We prove formally that the first order theory of algebraically closed fields enjoy quantifier elimination, and hence is decidable. This proof is organized in two modular parts. We ...
Quantifier reasoning in Satisfiability Modulo Theories (SMT) is a long-standing challenge. The practical method employed in modern SMT solvers is to instantiate quantified formulas...
We define a class of finite state automata acting on transfinite sequences, and use these automata to prove that no singular cardinal can be defined by a monadic second order formu...